Article
Multiplicatively Independent Integers and Dense Modulo 1 Sets of Sums
Authors
Abstract
Let c ∈ R, c > 0, β ∈ R and a1 > a2 > 1 and b1 > b2 > 1 be two distinct pairs of multiplicatively independent integers. If b1 > a1 and a2 > b2 or b1 < a1 and a2 < b2 then we prove that for every ξ1, ξ2, with at least one ξi irrational, there exists q ∈ N such that the set of sums {am 1 an 2 qξ1 + bm 1 bn 2 qξ2 + cm+nβ : m, n ∈ N}, is dense modulo 1 for all reals β.
Keywords
Density modulo 1, topological dynamics.
Citation
Urban, R. (2009). Multiplicatively independent integers and dense modulo 1 sets of sums. Uniform Distribution Theory, 4(1), 27–33.
R. Urban, “Multiplicatively independent integers and dense modulo 1 sets of sums,” Uniform Distribution Theory, vol. 4, no. 1, pp. 27–33, 2009.
Urban R. Multiplicatively independent integers and dense modulo 1 sets of sums. Uniform Distribution Theory. 2009;4(1):27–33.
Urban, R. (2009), ‘Multiplicatively independent integers and dense modulo 1 sets of sums’, Uniform Distribution Theory, 4(1), pp. 27–33.
Urban, Roman. “Multiplicatively Independent Integers and Dense Modulo 1 Sets of Sums.” Uniform Distribution Theory, vol. 4, no. 1, 2009, pp. 27–33.
Urban, Roman. “Multiplicatively Independent Integers and Dense Modulo 1 Sets of Sums.” Uniform Distribution Theory 4, no. 1 (2009): 27–33.
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Published by: Engineering Journals
